The classification of spaces of matrices of bounded rank is known to depend upon 'primitive' spaces, whose structure is considerably restricted. A characterisation of an infinite class of primitive spaces is given. The result is then applied to obtain a complete description of spaces whose matrices have rank at most 3. 1980 Mathematics subject classification (Amer. Math. Soc): 15 A 30, 15 A 03.

We present an algorithm for computing the 2-group e C` res F of narrow logarithmic divisor classes of degree 0 for number fields F . As an application, we compute in some cases the 2-rank of the wild kernel WK2(F ) and the 2-rank of its subgroup K ∞ 2 (F ) := ∩n≥1K 2 (F ) of infinite height elements in K2(F ).

We give infinite families of elliptic curves over Q such that each curve has infinitely many non-isomorphic quadratic twists of rank at least 4. Assuming the Parity Conjecture, we also give elliptic curves over Q with infinitely many non-isomorphic quadratic twists of odd rank at least 5.

Abstract The tensor rank decomposition, or canonical polyadic is the decomposition of a into sum rank-1 tensors. condition number measures sensitivity summands with respect to structured perturbations. Those are perturbations preserving that decomposed. On other hand, angular up scaling. We show for random rank-2 tensors expected value infinite wide range choices density. Under mild additional ...

A group $G$ has a finite special rank $r$ if every finitely generated subgroup of is by at most elements and there which exactly generators. If not such $r$, then we say that infinite rank. In this paper, study generalized radical non-abelian groups whose subgroups are transitively normal.

Abstract We prove effective equidistribution of horospherical flows in $\operatorname {SO}(n,1)^{\circ } / \Gamma $ when $\Gamma is geometrically finite and the frame flow exponentially mixing for Bowen–Margulis–Sullivan measure. also discuss settings which such an exponential result known to hold. As part proof, we show that Patterson–Sullivan measure satisfies some friendly like properties fi...

We prove geometric superrigidity for actions of cocompact lattices in semisimple Lie groups of higher rank on infinite dimensional Riemannian manifolds of nonpositive curvature and finite telescopic dimension.